1.

If `asinx+bcos(x+theta)+bcos(x-theta)=d ,`then the minimum value of `|costheta|`is equal to(a)`1/(2|b|)sqrt(d^2-a^2)`(b) `1/(2|a|)sqrt(d^2-a^2)`(c)`1/(2|d|)sqrt(d^2-a^2)`(d) none of these

Answer» `asinx+b[2cosxcostheta]=d`
`asinx+(2bcostheta)cosx=d`
`|d|<=sqrt(a^2+(2bcostheta)^2`
`|d|<=sqrt(a^2+4b^2cos^2theta`
`d^2<=a^2+4b^2cos^2theta`
`(d^2-a^2)/(4b^2)<=cos^2theta`
`|costheta|>=sqrt(d^2-a^2)/(2|B|)`
Option A is correct.


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